1. Field of the Invention
The present invention generally relates to a belt driving controller which controls driving of a belt wound around plural sustaining rollers, a belt rotating device using the belt driving controller, and an image forming apparatus using the belt rotating device.
2. Description of the Related Art
As an apparatus which uses belts, there is an image forming apparatus which uses a photoconductor belt, an intermediate transfer belt, a paper carrying belt, and so on. In the image forming apparatus, belt driving control at high accuracy is essential to obtain a high quality image. Especially, in a tandem type image forming apparatus having an image direct transfer system, which has a high image forming velocity and is suitable to be small sized, highly accurate driving control of a paper carrying belt which carries recording paper (recording medium) is required. In a color image forming apparatus, recording paper is carried by a carrying belt and is passed through plural image forming units, each of which forms a different single color image, along a paper carrying direction in order. Then, a color image in which single different color images are superposed can be obtained on the recording paper.
Referring to FIG. 12, an example of the tandem type image forming apparatus having an image direct transfer system using an electro-photographic technology is described. FIG. 12 is a diagram showing a part of the tandem type image forming apparatus which uses a direct image transfer system. As shown in FIG. 12, in the tandem type image forming apparatus, for example, image forming units 18K, 18C, 18M, and 18Y which form single color images of black, cyan, magenta, and yellow, respectively, are sequentially disposed in the paper carrying direction. Electrostatic latent images formed by laser exposure units (not shown) on the surfaces of photoconductor drums 40K, 40C, 40M, and 40Y are developed by the image forming units 18K, 18C, 18M, and 18Y, respectively, and toner images are formed. The toner images are transferred onto recording paper S which is carried by being adhered to a carrying belt 103 by an electrostatic force so that the toner images are superposed in order. Then toners are fused by a fuser (fixing unit) 25 and a color image is formed on the recording paper S. The carrying belt 103 is wound around a driving roller 215 and a driven roller 214 both of which are disposed in parallel with suitable tension. The driving roller 215 is rotated with a predetermined rotation velocity by a driving motor (not shown) and then the carrying belt 103 is moved endlessly with a predetermined velocity. The recording paper S is fed to the image forming units 18K, 18C, 18M, and 18Y with predetermined timing by a paper feeding mechanism (not shown) and is carried at the same velocity as the moving (linear) velocity of the carrying belt 103, and is passed through the image forming units 18K, 18C, 18M, and 18Y in order.
In the tandem type image forming apparatus, when the moving velocity of the recording paper S, that is, the moving velocity of the carrying belt 103 is not sustained at a constant velocity, color registration errors occur. The color registration errors occur when the transferring position of a color image which is superposed on the recording paper S is shifted relative to different color images. When the color registration errors occur, for example, fine-line images formed by superposing plural color images are blurred, and a white part occurs at a position near a contour of a black letter image formed in a background image formed by superposing plural color images. In FIG. 12, the description of the reference number 62 is omitted.
FIG. 13 is a diagram showing a part of a tandem type image forming apparatus which uses an intermediate image transfer system. In the tandem type image forming apparatus shown in FIG. 13, a single color image formed on the surface of each of the photoconductor drums 40K, 40C, 40M, and 40Y in the corresponding image forming units 18K, 18C, 18M, and 18Y is temporarily transferred onto an intermediate transfer belt 10 so that the single color images are sequentially superposed, and the transferred image is recorded on recording paper. That is, the tandem type image forming apparatus shown in FIG. 13 uses the intermediate image transfer system. In this apparatus, when the moving velocity of the intermediate transfer belt 10 is not maintained at a constant velocity, the color registration errors also occur.
In FIG. 13, the description of the reference numbers 9, 14, 15, 16, 24, 25, 49, and 62 is omitted.
In addition to the tandem type image forming apparatuses, in an image forming apparatus which uses belts in a recording medium carrying member which carries a recording medium, a photoconductor body which carries an image to be transferred onto the recording medium, and an image carrier such as an intermediate transfer body, when the moving velocity of a belt is not maintained at a constant value, banding occurs. The banding is image density errors caused by a fluctuation of belt moving velocity while an image is being transferred. That is, when the belt moving velocity is relatively fast, a part of a transferred image is enlarged in the belt moving direction from the original image; on the contrary, when the belt moving velocity is relatively slow, a part of the transferred image is reduced in the belt moving direction from the original image. Therefore, the density of the enlarged part of the image becomes thin and the density of the reduced part of the image becomes thick. As a result, the image density errors occur in the belt moving direction, that is, the banding occurs. When a light single color image is formed, the banding is especially noticeable.
The moving velocity of the belt fluctuates caused by various factors; as one of them, there is thickness unevenness of a belt in the belt moving direction when the belt is a single layer belt. The thickness unevenness of the belt along the belt moving direction (belt circumference direction) is caused when a belt is formed by a centrifugal burning method using a cylindrical die. In a case where the thickness unevenness exists in the belt, when the thick part of the belt is wound around the driving roller which drives the belt, the belt moving velocity becomes faster; on the contrary, when the thin part of the belt is wound around the driving roller, the belt moving velocity becomes slower. That is, the moving velocity of the belt fluctuates. The reasons are described below in detail.
FIG. 14 is a graph showing an example of the belt thickness fluctuation in the moving direction of the intermediate transfer belt 10 shown in FIG. 13. In FIG. 14, the horizontal line shows a belt position in one round of a belt in which the belt circumference length is transformed into the angle of 2Π rad. The vertical line shows a belt thickness fluctuation (deviation) (μm) from a reference value determined to be 0. In this, actually, the reference value is the belt thickness average value (100 μm) in the belt circumference direction.
In the description of the embodiment of the present invention, in a belt which has the belt thickness unevenness, the belt thickness deviation distribution of the one round in the belt circumference direction is called the belt thickness fluctuation. Therefore, the belt thickness unevenness and the belt thickness fluctuation are described in detail. The belt thickness unevenness shows a belt thickness deviation distribution measured by a film thickness measuring instrument and exists in the belt circumference direction (belt moving direction) and the belt width direction (driving roller axle direction). The belt thickness fluctuation shows a belt thickness deviation distribution caused by the fluctuations of a belt rotation cycle which affects a belt moving velocity for the rotation angle velocity (angular velocity) of the driving roller and the rotation angle velocity of the driven roller for the belt moving velocity where the belt is installed with a belt driving controller.
FIG. 15 is an enlarged view of a part of a belt wound around a driving roller viewed from the axle direction of the driving roller.
In FIG. 15, the moving velocity of a belt 103 is determined by a PLD (pitch line distance) which distance is from the surface of a driving roller 105 to the belt pitch line. When the belt 103 is a single layer belt whose material is uniform and the absolute values of the stretch of the inner and outer circumferences of the belt 103 are almost equal, the PLD corresponds to the distance from the center of the thickness of the belt 103 to the surface of the driving roller 105 (the inner circumference surface of the belt 103) (Bt). Therefore, in a case of the single layer belt, the relationship between the PLD and the belt thickness approximately becomes constant; consequently, the moving velocity of the belt 103 can be determined by the belt thickness fluctuation. However, in a plural-layer belt, since the stretch of the hard layer and the stretch of the soft layer are different from each other, the PLD becomes a distance between a position deviated from the center of the thickness of the belt 103 and the surface of the driving roller 105. Further, in some cases, the PLD changes due to a belt winding angle on (angular range of contact with) the driving roller 105.PLD=PLDave+ƒ(d)  [Equation 1]Where the PLDave is an average value of the PLDs in one round of the belt. For example, in a case of a single layer belt whose average thickness is 100 μm, the PLDave is 50 μM. The f(d) is a function showing a fluctuation of the PLD in one round of the belt, and “d” is a position from a reference on the belt circumference (phase when one round of the belt is defined as 2Π). The f(d) has a high correlation with the belt thickness fluctuation shown in FIG. 14, and a periodic function in which one round of the belt is a period. When the PLD fluctuates in the belt circumference direction, the belt moving velocity or the belt moving distance fluctuates for the rotation angle velocity or the rotation angle displacement of the driving roller, or the rotation angle velocity or the rotation angle displacement of the driven roller fluctuates for the belt moving velocity or the belt moving distance. In FIG. 15, in order to describe the PLD, the reference numbers of the corresponding belt and driving roller are not the same as those shown in FIGS. 12 and 13.
A relationship between the belt moving velocity V and the rotation angle velocity ω of the driving roller 105 is shown in Equation 2.V={r+PLDave+κƒ(d)}ω  [Equation 2]
Where “r” is the radius of the driving roller 105. The degree to which the f(d) showing the fluctuation of the PLD influences the relationship between the belt moving velocity or the belt moving distance and the rotation angle velocity or the rotation angle displacement of the roller may change depending on belt contacting conditions and a belt winding amount onto the roller. The influencing degree is shown by a PLD fluctuation effective coefficient “κ”.
In the description of the present invention, the range surrounded by { } in Equation 2 is called a roller effective radius. Especially, the constant part (r+PLDave) is called a roller effective radius R. The f(d) is called a PLD fluctuation.
Since the PLD fluctuation f(d) exists in Equation 2, it is understandable that the relationship between the belt moving velocity V and the rotation angle velocity ω of the driving roller 105 changes.
That is, even if the driving roller 105 rotates at a constant rotation angle velocity ω(=constant), the belt moving velocity V is changed by the PLD fluctuation f(d). For example, in a case of a single layer belt, when a part of the belt whose thickness is greater than the average belt thickness is wound around the driving roller 105, the PLD fluctuation f(d) which has a high correlation with the thickness deviation of the belt 103 is a positive value and the roller effective radius increases. Consequently, even if the driving roller 105 rotates at a constant rotation angle velocity (ω=constant), the belt moving velocity V increases. On the contrary, when a part of the belt whose thickness is less than the average belt thickness is wound around the driving roller 105, the PLD fluctuation f(d) is a negative value and the roller effective radius decreases. Consequently, even if the driving roller 105 rotates at a constant rotation angle velocity (ω=constant), the belt moving velocity V decreases.
As described above, even if the rotation angle velocity ω of the driving roller 105 is constant, the belt moving velocity V does not become constant due to the PLD fluctuation f(d). Therefore, if it is attempted to control the driving of the belt 103 by only the rotation angle velocity ω of the driving roller 105, the belt 103 cannot be driven at a desired constant moving velocity.
Further, the relationship between the belt moving velocity V and the rotation angle velocity of the driven roller is the same as that between the belt moving velocity V and the rotation angle velocity ω of the driving roller 105. That is, when the rotation angle velocity of the driven roller is detected by a rotary encoder and the belt moving velocity V is obtained by the detected rotation angle velocity, Equation 2 can be used. For example, in a case of a single layer belt, when a part of the belt whose thickness is greater than the average belt thickness is wound around the driven roller, similar to the case of the driving roller 105, the PLD fluctuation f(d) which has a high correlation with the thickness deviation of the belt 103 is a positive value and the roller effective radius increases. Consequently, even if the belt 103 moves with a constant moving velocity (V=constant), the rotation angle velocity of the driven roller decreases. On the contrary, when a part of the belt whose thickness is less than the average belt thickness is wound around the driven roller, the PLD fluctuation f(d) is a negative value and the roller effective radius decreases. Consequently, even if the belt 103 moves at a constant moving velocity, the rotation angle velocity of the driven roller increases.
As described above, even if the moving velocity of the belt 103 is constant, the rotation angle velocity of the driven roller does not become constant due to the PLD fluctuation f(d). Therefore, even if it is attempted to control the driving of the belt 103 by the rotation angle velocity of the driven roller, the belt 103 cannot be driven at a desired moving velocity.
As a belt driving control technology which considers the PLD fluctuation f(d), an image forming apparatus is disclosed in Patent Documents 1 and 2.
In the image forming apparatus of Patent Document 1, before installing a belt in the image forming apparatus, which belt is formed by a centrifugal forming method in which the PLD fluctuation f(d) is likely to occur in a sine wave in one round of a belt, a thickness profile (belt thickness unevenness) of all the circumference of the belt is measured beforehand in the manufacturing process, and the measured data are stored in a flash ROM. In the image forming apparatus, a reference mark is attached to a home position that is a reference position to match the phase of the profile data of the circumference thickness with the phase of actual belt thickness unevenness. The belt driving control is executed so as to cancel the fluctuation of the belt moving velocity caused by the belt thickness unevenness by detecting the belt thickness unevenness at the reference mark.
In the image forming apparatus of Patent Document 2, a pattern for detection is formed on a belt, the pattern is detected by a detection sensor, and a periodic fluctuation of the belt moving velocity is detected by using the pattern. The belt driving control is executed to cancel the fluctuation of the belt moving velocity caused by the belt thickness fluctuation based on the above detection.
However, in the image forming apparatus of Patent Document 1, it is required to have a process which measures the belt thickness unevenness in the manufacturing process of the belt and a highly accurate thickness measuring instrument is required in the measuring process. Consequently, the manufacturing cost largely increases. In addition, when the belt is changed to a new one, it is required to input the thickness profile data of the new belt in the apparatus. Further, in the image forming apparatus, since the belt thickness unevenness is used without using the PLD fluctuation f(d), in a case of the single layer belt, the belt driving control can be accurately performed, but the belt driving control cannot be performed accurately in a case of the plural-layer belt.
In the image forming apparatus described in Patent Document 2, in order to detect the fluctuation of the belt moving velocity, it is required to form the pattern for detection in at least one round of the belt. Therefore, a large amount of toner is consumed to form the pattern for detection. Especially, in order to detect the fluctuation of the belt moving velocity at high accuracy, when an average value of fluctuation data of the belt moving velocity is obtained by measuring the belt moving velocities of the belt circumference plural times and the average value is used as the fluctuation of the belt moving velocity, the plural patterns for detection of the plural belt circumferences must be formed, and the plural measurements of the belt circumference consume the toner greatly.
In patent document 3, the inventor of the present invention discloses a belt driving controller which can solve the above problems. In the belt driving controller, the rotation angle displacement or the rotation angle velocity of a driven sustaining rotation body is detected, and an alternating current component of the rotation angle velocity of the driven sustaining rotation body having a frequency corresponding to the periodic thickness fluctuation in the belt circumference direction is extracted from the detected data. The amplitude and the phase of the extracted alternating current component correspond to the amplitude and the phase of the periodic thickness fluctuation in the circumference direction of the belt. Therefore, based on the amplitude and the phase of the extracted alternating current component, the rotation angle velocity of a driving sustaining rotation body is controlled to be low at the timing when a thick part of the belt contacts the driving sustaining rotation body and the rotation angle velocity of the driving sustaining rotation body is made high at the timing when a thin part of the belt contacts the driving sustaining rotation body.
According to this technology, the belt can be driven at a desired moving velocity without suffering any influence of the thickness fluctuation in the circumference direction of the belt. Further, it is not necessary to have a process for measuring the belt thickness unevenness in the belt manufacturing process; therefore, the manufacturing cost does not increase, while the cost increases in Patent Document 1. In addition, it is not necessary to have a process for inputting thickness profile data in the apparatus when the belt is changed to a new one. Further, it is not necessary to form a pattern for detection, while it is needed in Patent Document 2. Therefore, toner is not consumed for the belt driving control.
However, in the belt driving controller of Patent Document 3, since the belt thickness fluctuation is approximated by a periodic function; namely, a sine function (cosine function), it is necessary to know the belt thickness fluctuation that occurs in one round of the belt beforehand. That is, it is necessary to know beforehand whether the frequency component included in the belt thickness fluctuation is only a basic frequency component having a cycle equal to the cycle of one round of the belt, or includes a high-frequency component. In addition, in a case of a belt having a seam part, the seam part may thicker than the other parts; then, the belt thickness fluctuation may occur at the seam part. This kind of belt thickness fluctuation is difficult to be approximated by the periodic function.
[Patent Document 1] Japanese Laid-Open Patent Application No. 2000-310897
[Patent Document 2] Japanese Patent No. 3186610
[Patent Document 3] Japanese Laid-Open Patent Application No. 2004-123383 (Japanese Patent No. 3677506)
In order to solve the above problems, the inventor of the present invention discloses a belt driving controller in Japanese Priority Patent Application No. 2005-046548 (hereinafter referred to as a precedent application). The belt driving controller controls driving a belt wound around plural sustaining rotation bodies including a driven sustaining rotation body which are rotated together with a movement of the belt and a driving sustaining rotation body which transfers a driving force to the belt. The belt driving controller includes a control unit. The control unit executes the driving control of the belt so that a moving velocity fluctuation of the belt caused by a PLD fluctuation in the belt circumference direction becomes small, based on rotation information of rotation angle displacement or rotation angle velocities in two of the sustaining rotation bodies in the plural sustaining rotation bodies, in which two sustaining rotation bodies the diameters are different from each other and/or the degrees of the PLDs of belt parts wound around the two rollers influencing a relationship between the belt moving velocity and the rotation angle velocities of the two sustaining rotation bodies are different from each other.
In addition, in the precedent application, a PLD fluctuation recognition method which calculates a control value to restrain the moving velocity fluctuation of the belt is described. In the calculation, an adding process is executed. In the adding process, to the two rotation fluctuation information items whose phases are different from each other included in the rotation information of one or both of the two sustaining rotation bodies, a belt passing through period (delaying period) which is required for the belt to move the distance between the two sustaining rotation bodies on a belt moving route and a gain based on the degrees of the two sustaining rotation bodies are added. The adding process is repeated “n” times (n≧1), and in the adding process, as the gain at the nth adding process, the 2n−1 power of the gain G of the first adding process is used, and as the delay period of the nth adding process, the 2n−1 times of the delay period of the first adding process is used.
However, in the adding process of the precedent application, the delay period may become large depending on the positions where the two sustaining rotation bodies are disposed and the moving direction of the belt. When the delay period becomes large, the capacity of a memory unit which is needed for the calculation becomes large. Consequently, a period for calculating a desirable control value becomes large. For example, in the adding process of the precedent application, a calculation block shown by Exp(−τs) corresponds to a memory unit for generating a delay of a phase difference “τ” (delay period), and plural memory units are disposed. When data are sequentially stored in the plural memory units fully, the desirable control value is calculated. Therefore, the calculation period until the desirable control value is calculated greatly depends on the phase difference “τ”. The Exp(−τs) is shown in FIG. 3, and the contents in FIG. 3 are described below in detail in the embodiments of the present invention.
In FIG. 6, a part of a belt rotating device is shown. The belt rotating device includes a roller 101 having a small diameter, and a roller 102 having a large diameter, and a belt moving direction is shown by an arrow A. The delay period is a time in which a belt 103 is moved by a distance 205 shown by an alternate long and short dash line. That is, the delay period is the time in which the belt 103 is moved from the roller 101 to the roller 102 along the belt moving direction A. When the belt movement is reversed, the delay period is a time in which the belt is moved by a distance 251 shown by a continuous line from the roller 101 to the roller 102. Generally, the phase difference “τ” corresponds to the delay period. When the delay period is long, the calculation time becomes long and the capacity of the memory unit must be large. In belt driving control in the belt rotating device, the contents in FIG. 6 are described below in detail in the embodiments of the present invention.